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Edilberto O. Silva

Publications and source records attributed to Edilberto O. Silva.

114 records · Page 7Linked to original sources
arXiv2015

Influence of spatially varying pseudo-magnetic field on a 2D electron gas in graphene

The effect of a varying pseudo-magnetic field, which falls as $1/x^2$, on a two dimensional electron gas in graphene is investigated. By considering the second order Dirac equation, we show that its correct general solution is that which might present singular wavefunctions since such field induced by elastic deformations diverges as $x\rightarrow0$. We show that only this consideration yields the known relativistic Landau levels when we remove such elastic field. We have observed that the zero Landau level fails to develop for certain values of it. We then speculate about the consequences of these facts to the quantum Hall effect on graphene. We also analyze the changes in the relativistic cyclotron frequency. We hope our work being probed in these contexts, since graphene has great potential for electronic applications.

cond-mat.mes-hall↗
arXiv2014

Effects of spin on the dynamics of the 2D Dirac oscillator in the magnetic cosmic string background

In this work the dynamics of a 2D Dirac oscillator in the spacetime of a magnetic cosmic string is considered. It is shown that earlier approaches to this problem have neglected a $δ$ function contribution to the full Hamiltonian, which comes from the Zeeman interaction. The inclusion of spin effects leads to results which confirm a modified dynamics. Based on the self-adjoint extension method, we determined the most relevant physical quantities, such as energy spectrum, wave functions and the self-adjoint extension parameter by applying boundary conditions allowed by the system.

hep-th↗
arXiv2014

Remarks on the Dirac oscillator in $(2+1)$ dimensions

In this work the Dirac oscillator in $(2+1)$ dimensions is considered. We solve the problem in polar coordinates and discuss the dependence of the energy spectrum on the spin parameter $s$ and angular momentum quantum number $m$. Contrary to earlier attempts, we show that the degeneracy of the energy spectrum can occur for all possible values of $sm$. In an additional analysis, we also show that an isolated bound state solution, excluded from Sturm-Liouville problem, exists.

hep-th↗
arXiv2014

The 2D $κ$-Dirac oscillator

In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the $κ$-Poincaré-Hopf algebra is considered. The problem is formulated using the $κ$-deformed Dirac equation. The resulting theory reveals that the energies and wave functions of the oscillator are modified by the deformation parameter.

hep-th↗
arXiv2014

Goldbach conjecture sequences in quantum mechanics

We show that there is a correspondence between Goldbach conjecture sequences (GCS) and expectation values of the number operator in Fock states. We demonstrate that depending on the normalization or not of Fock state superpositions, we have sequences that are equivalent and sequences that are not equivalent to GCS. We propose an algorithm where sequences equivalent to GCS can be derived in terms of expectation values with normalized states. Defining states whose projections generate GCS, we relate this problem to eigenstates of quantum harmonic oscillator and discuss Fock states directly associated to GCS, taking into account the hamiltonian spectrum and quantum vacuum fluctuations. Finally, we address the problems of degeneracy, maps associating GCS and Goldbach partitions.

physics.gen-ph↗